1. Field of the Invention
This invention relates to signal conversion devices.
2. Description of the Prior Art
Recently, attention is being paid to AD (analog-digital) and DA (digital-analog) conversion techniques, so-called .DELTA.-.SIGMA. modulation systems, which are suitable for, for example, acoustic measurement or the like, employing over-sampling methods to obtain enough dynamic range in a low frequency region (for example, the frequency region of around 20 KHz which is within the human audible region) by concentrating spectrum distribution of quantization noise in a high frequency region. Such .DELTA.-.SIGMA. modulation systems are described in detail in, for example, Nikkei Electronics 1988. 8. 8. (No. 453), pp. 216-220, or Radio Technology September 1987, pp. 37-44, and thus detailed description thereof will be omitted here.
.DELTA.-.SIGMA. modulators differentiate quantization noise, Q, which is generated in quantizers (hereinafter called partial quantizers) contained therein, and thereby a desirable dynamic range is obtained by a fewer number of bits in a low region where the quantization noise is supressed. The transfer characteristic of the .DELTA.-.SIGMA. modulator with k order is represented in the below formula (1) with an input X, an output Y, and noise Q of partial quantizers. EQU Y=X+(1-Z.sup.-1).sup.k *Q (1)
The .DELTA.-.SIGMA. modulator represented by formula (1) may be realized by various methods, but all which have final outputs described by formula (1) are called .DELTA.-.SIGMA. modulators here. (1-Z.sup.-1).sup.k in formula (1) shows a differential characteristic, and if the partial quantizers have a straight-line quantization characteristic and have a quantized value of 2.sup.m, this 2.sup.m value can be encoded to m bits.
Under the condition of a quantization step width of the partial quantizers being .DELTA. and the quantization noise always being distributed within the range of .+-..DELTA./2, the quantization noise, Q, may be regarded as white noise distributed in the range of .+-..DELTA./2, with their power (quantization noise power) being .DELTA..sup.2 /12. If an operation clock of the .DELTA.-.SIGMA. modulators (a sampling frequency) is .function..sub.s, the above power can be regarded as being distributed uniformly in a band region up to .function..sub.s /2 (the Nyquist frequency), and thus a power density thereof is .DELTA..sup.2 /12*2/.function..sub.s. On the other hand, an amplitude characteristic of the differential characteristic (1-Z.sup.-1).sup.k becomes .vertline.(1-Z.sup.-1).sup.k .vertline.=2.sup.k * sin.sup.k (.pi..function./.function..sub.s) when Z.sup.-1 equals e.sup.equals e.sup.-j.spsp.2.pi..function./.function..sub.s, and spectrum N.function. of the differentiated quantization noise (1-Z.sup.-1).sup.k *Q becomes ##EQU1## The spectrum N.function. shown in this formula is a curve as shown in FIG. 12. The input X here is assumed to be a sine wave.
Next, with regard to FIGS. 9-11, the principle of a secondary .DELTA.-.SIGMA. modulator will be described.
An inner structure of an AD converter AD1 (a secondary .DELTA.-.SIGMA. modulator) in FIG. 9 comprises, as shown in FIG. 11, two integrators S1 and S2 each connected one step ahead to a comparator (quantizer) Q1, and a feedback loop which goes from an output of the comparator Q1 to each input of these integrators S1 and S2 through a one step delay element Z.sup.-1 and a DA converter. A D flip-flop DFF1 is connected to the output of the comparator Q1 to establish the timing of the digital output (a PDM wave: Pulse Density Modulation).
The above structure may be represented as Y=X+(1-Z.sup.-1).sup.2 *Q by the above formula (1) of the transfer function. It presents, as shown in FIG. 11, signal elements contained in the output being equal to the input signal (in this case, a sine wave) by providing the secondary integrators (that is, the two integrators S1 and S2) preceding the comparator Q1, and also only a quantization noise, Q, taking the form of a secondary finite difference.
Actually, in FIGS. 9 and 11, when an output is observed by a high performance spectrum analyzer or the like with an input signal of 1 KHz, a sine wave of -40 dB, and a sampling frequency .function..sub.s of, for example, 6 MHz, the wave form shown in FIG. 10 can be seen. Also, the quantization noise, Q, may be made white noise which is unrelated to the input signal, by adding to the input signal a uniformly distributed random variable as a so-called dither (a kind of white noise), before quantization and then substracting the same dither after the quantization, as shown in phantom in FIGS. 9 and 11, the wave shown in phantom in FIG. 10, being seen with output observed in the same way as above. Conversion precision can be improved by addition/subtraction of a dither with larger amplitude in the above, and similar effects as addition/subtraction of the dither may be obtained in a low frequency region even without subtraction, by adding to the input signal the dither (in this case, a so-called "colored noise", noise which concentrates in a specific frequency region) concentrated by a band pass filter or the like in a high frequency region (for example, 120 KHz-200 KHz) (see Yamazaki, "Application of a Large Amplitude Dither to Quantization of Wide Band Region Acoustic Signals", Onkyogakukaisi 39(7) pp. 452-462 (1983), and Nishitoba, Ohtani, Asotani, Yamazaki, and Itoh, "Improvement of AD Conversion Precision by Large Amplitude Dithers and High Speed Sampling", Denonkensi EA82-72 (1983)).
Therefore, even in doing like the above, enough dynamic range (S/N for a full scale sine wave: that is, a relation between a dynamic range DR and quantization bit number m is generally represented by DR=6.02 m+1.76(dB)) would not be ensured across a wide band region in the low frequency region.
Generally, a distribution of the quantization noise concentrates in a higher region by raising orders of the .DELTA.-.SIGMA. modulators, but inner circuits become unstable in the .DELTA.-.SIGMA. modulators of the third order and over.